What is the simplified expression for the expression below? -1\/5(5x + 20) – 1\/4(4x – 28)<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Correct Answer:<\/strong> \u22121\/5(5x+20)\u22121\/4(4x\u221228)=\u2212x\u22123-1\/5(5x + 20) – 1\/4(4x – 28) = -x – 3<\/p>\n\n\n\n Step-by-Step Simplification:<\/strong><\/p>\n\n\n\n We are given the expression: \u221215(5x+20)\u221214(4x\u221228)-\\frac{1}{5}(5x + 20) – \\frac{1}{4}(4x – 28)<\/p>\n\n\n\n Distribute \u221215-\\frac{1}{5} into the first parentheses: \u221215(5x+20)=\u221215\u22c55x\u221215\u22c520=\u2212x\u22124-\\frac{1}{5}(5x + 20) = -\\frac{1}{5} \\cdot 5x – \\frac{1}{5} \\cdot 20 = -x – 4<\/p>\n\n\n\n Distribute \u221214-\\frac{1}{4} into the second parentheses: \u221214(4x\u221228)=\u221214\u22c54x+14\u22c528=\u2212x+7-\\frac{1}{4}(4x – 28) = -\\frac{1}{4} \\cdot 4x + \\frac{1}{4} \\cdot 28 = -x + 7<\/p>\n\n\n\n Now add the two parts together: (\u2212x\u22124)+(\u2212x+7)=\u2212x\u22124\u2212x+7(-x – 4) + (-x + 7) = -x – 4 – x + 7<\/p>\n\n\n\n Combine like terms:<\/p>\n\n\n\n So we have: \u22122x+3-2x + 3<\/p>\n\n\n\n But let\u2019s double-check the original work. Oops! There’s a mistake<\/strong> here.<\/p>\n\n\n\n Wait: in the original distribution<\/em>, we got:<\/p>\n\n\n\n Then total expression is: (\u2212x\u22124)+(\u2212x+7)=\u2212x\u22124\u2212x+7=\u22122x+3(-x – 4) + (-x + 7) = -x – 4 – x + 7 = -2x + 3<\/p>\n\n\n\n So the correct simplified expression<\/strong> is: \u22122x+3\\boxed{-2x + 3}<\/p>\n\n\n\n \u22122x+3\\boxed{-2x + 3}<\/p>\n\n\n\n To simplify an algebraic expression involving distribution and like terms, we follow key steps: distribute<\/strong>, then combine like terms<\/strong>.<\/p>\n\n\n\n We begin with the expression: \u221215(5x+20)\u221214(4x\u221228)-\\frac{1}{5}(5x + 20) – \\frac{1}{4}(4x – 28)<\/p>\n\n\n\n Distributive property means multiplying the term outside the parentheses with each term inside. So, distributing \u221215-\\frac{1}{5} over (5x+20)(5x + 20), we get: \u221215\u22c55x=\u2212x,\u221215\u22c520=\u22124,giving \u2212x\u22124.-\\frac{1}{5} \\cdot 5x = -x,\\quad -\\frac{1}{5} \\cdot 20 = -4,\\quad \\text{giving } -x – 4.<\/p>\n\n\n\n Next, distribute \u221214-\\frac{1}{4} over (4x\u221228)(4x – 28): \u221214\u22c54x=\u2212x,\u221214\u22c5(\u221228)=+7,giving \u2212x+7.-\\frac{1}{4} \\cdot 4x = -x,\\quad -\\frac{1}{4} \\cdot (-28) = +7,\\quad \\text{giving } -x + 7.<\/p>\n\n\n\n Now combine both results: (\u2212x\u22124)+(\u2212x+7)(-x – 4) + (-x + 7)<\/p>\n\n\n\n Combine like terms:<\/p>\n\n\n\n Final simplified expression: \u22122x+3-2x + 3<\/p>\n\n\n\n This process highlights the importance of careful distribution and correct sign handling. Distributing negatives and fractions often trips up students, but remembering to apply the distributive property to each term inside the parentheses, and to carefully track positive\/negative signs, leads to success.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the simplified expression for the expression below? -1\/5(5x + 20) – 1\/4(4x – 28) The correct answer and explanation is: Correct Answer: \u22121\/5(5x+20)\u22121\/4(4x\u221228)=\u2212x\u22123-1\/5(5x + 20) – 1\/4(4x – 28) = -x – 3 Step-by-Step Simplification: We are given the expression: \u221215(5x+20)\u221214(4x\u221228)-\\frac{1}{5}(5x + 20) – \\frac{1}{4}(4x – 28) Step 1: Distribute the fractions Distribute […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-20306","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20306","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=20306"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20306\/revisions"}],"predecessor-version":[{"id":20307,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20306\/revisions\/20307"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=20306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=20306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=20306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Distribute the fractions<\/h3>\n\n\n\n
Step 2: Combine like terms<\/h3>\n\n\n\n
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\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
\n\n\n\n300-Word Explanation:<\/h3>\n\n\n\n
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